Weak brill-noether for rational surfaces

Izzet Coskun, Jack Huizenga

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations

Abstract

A moduli space of sheaves satisfies weak Brill-Noether if the general sheaf in the moduli space has no cohomology. Göttsche and Hirschowitz prove that on P2 every moduli space of Gieseker semistable sheaves of rank at least two and Euler characteristic zero satisfies weak Brill-Noether. In this paper, we give sufficient conditions for weak Brill-Noether to hold on rational surfaces. We completely characterize Chern characters on Hirzebruch surfaces for which weak Brill-Noether holds. We also prove that on a del Pezzo surface of degree at least 4 weak Brill-Noether holds if the first Chern class is nef.

Original languageEnglish (US)
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages81-104
Number of pages24
DOIs
StatePublished - Jan 1 2018

Publication series

NameContemporary Mathematics
Volume712
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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    Coskun, I., & Huizenga, J. (2018). Weak brill-noether for rational surfaces. In Contemporary Mathematics (pp. 81-104). (Contemporary Mathematics; Vol. 712). American Mathematical Society. https://doi.org/10.1090/conm/712/14343